Question: Simplify the following expression: $q = \dfrac{5a^2 - 10a - 75}{a - 5} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ q =\dfrac{5(a^2 - 2a - 15)}{a - 5} $ Then we factor the remaining polynomial: $a^2 {-2}a {-15} $ ${-5} + {3} = {-2}$ ${-5} \times {3} = {-15}$ $ (a {-5}) (a + {3}) $ This gives us a factored expression: $\dfrac{5(a {-5}) (a + {3})}{a - 5}$ We can divide the numerator and denominator by $(a + 5)$ on condition that $a \neq 5$ Therefore $q = 5(a + 3); a \neq 5$